Factorisation in stopping-time Banach spaces: Identifying unique maximal ideals

Stopping-time Banach spaces is a collective term for the class of eventually null integrable processes that are defined in terms behaviour stopping times with respect to some fixed filtration. From point view space theory, these many regards resemble classical such as L1 or C(Δ), but unlike these, they do have unconditional bases. In present paper, we study canonical bases stopping-time relation factorising identity operator thereon. Since work exclusively dyadic-tree filtration, this setup enables us tree-indexed rather than directly stochastic processes. En route factorisation results, develop general criteria allow one deduce uniqueness maximal ideal algebra operators on space. These applicable (mixed-norm) Lp-spaces, BMO, SL∞, and others.